1. Field of the Invention
The present invention relates to a digital filter and, more particularly, to an IIR (Infinite Impulse Response) digital filter.
2. Related Art
In recent years, a digital filter which realizes the functions of an analog low pass filter, a band pass filter, and a high pass filter by a region of digital signal processes has been fairly widely used.
The digital filter is mainly classified into an FIR type (Finite Impulse Response type) (non-recursive type) and an IIR type (recursive type). In the case of the IIR type, it is known that when the digital filter is constructed by an arithmetic unit of a finite word length, even if an amplitude level of an input signal is set to zero after a certain time, an amplitude of an output of the digital filter is not attenuated to zero but an amplitude component is output (such a state is called a limit cycle phenomenon).
Such an amplitude component output is observed as a residual noise when a zero level signal is input to the IIR digital filter.
An amplitude level (dead band amplitude level DB) of a limit cycle signal of a primary IIR digital filter whose difference equation is given by the following equation as an example. EQU y(t)=-.alpha..multidot.y(t-1)+x(t) EQU (t=1, 2, . . . , .vertline..alpha..vertline.&lt;1) (1)
is as follows. EQU .vertline.y.sub.Q (t-1).vertline..ltoreq.(1/2).multidot.2.sup.-b /(1-.vertline..alpha..vertline.)
y.sub.Q (t): quantized output signal, PA1 2.sup.-b : quantizing step, PA1 b: quantized bit number (2)
For instance, as shown in FIG. 6, it is assumed that there is a digital low pass filter in which after an input analog signal was converted into a digital signal by an A/D converter 10, the digital signal is input to an IIR digital filter 12 and only a low band component is allowed to pass, and the digital signal is further converted into the original analog signal by a D/A converter 14 and the analog signal is output. In this case, as shown in FIG. 7, in a range in which an amplitude level of an input signal is set to a predetermined critical input level C or higher, the amplitude level of the input signal and the amplitude level of the output signal proportionally change. However, when the amplitude level of the input signal is set to the critical input level C or lower, even if the input level decreases, the amplitude level of the output signal does not decrease and an output which is independent of the input shown by the above equation appears.
As will be understood from the equation (2), as the quantizing step is small, the dead band output amplitude level DB also decreases and, when .alpha.&lt;1/2, no limit cycle occurs.
However, when the quantizing step is reduced, the number of bits which are necessary for operations increases, so that a construction of the digital filter enlarges in size and becomes complicated.
On the other hand, if a coefficient of the digital filter is held to a value of 0.5 or less such as not to cause a limit cycle, this means that the filter characteristics are limited.
The invention is made in consideration of the conventional problems as mentioned above and it is an object of the invention to provide a digital filter in which a limit cycle can be suppressed for an IIR digital filter without increasing the number of bits nor limiting the filter characteristics.
Another object of the invention is to provide a filter apparatus of a simple construction.
Further another object of the invention is to enable a limit cycle to be effectively suppressed for a cascade connected type IIR digital filter without increasing the number of bits nor limiting the characteristics.